The Taylors have purchased a $170,000 house. They made an initial down payment of $30,000 and secured a mortgage with interest charged at the rate of 9%/year on the unpaid balance. Interest computations are made at the end of each month. If the loan is to be amortized over 30 years, what monthly payment will the Taylors be required to make? (Round your answer to the nearest cent.)

Question

The Taylors have purchased a $170,000 house. They made an initial down payment of $30,000 and secured a mortgage with interest charged at the rate of 9%/year on the unpaid balance. Interest computations are made at the end of each month. If the loan is to be amortized over 30 years, what monthly payment will the Taylors be required to make? (Round your answer to the nearest cent.)

Answer 1

To calculate the monthly payment the Taylors need to make, we can use the formula for a fixed-rate mortgage payment. The formula is:

P = (Pv * r) / (1 - (1 + r)^(-n))

Where:
P = monthly payment
Pv = present value of the loan (loan amount minus down payment)
r = monthly interest rate
n = number of monthly payments

Let's calculate it step by step:

1. Calculate the present value of the loan (Pv):
Pv = loan amount - down payment
Pv = $170,000 - $30,000
Pv = $140,000

2. Convert the interest rate to monthly rate:
r = annual interest rate / 12 / 100
r = 9% / 12 / 100
r = 0.0075

3. Calculate the number of monthly payments:
n = number of years * 12
n = 30 * 12
n = 360

4. Calculate the monthly payment (P):
P = ($140,000 * 0.0075) / (1 - (1 + 0.0075)^(-360))

Now, let's plug in the values and calculate the monthly payment:

P = ($140,000 * 0.0075) / (1 - (1 + 0.0075)^(-360))
P ≈ $1,061.14

Therefore, the Taylors will be required to make a monthly payment of approximately $1,061.14.

Answer 2

To calculate the monthly payment required for the mortgage, we need to use the formula for calculating the monthly payment of an amortizing loan:

M = (P * r) / (1 - (1 + r)^(-n))

Where:
M = Monthly payment
P = Principal amount (loan amount - down payment)
r = Monthly interest rate (annual interest rate / 12)
n = Total number of monthly payments (30 years * 12 months per year)

Let's calculate each value step by step:

1. Principal amount (P):
P = $170,000 - $30,000 = $140,000

2. Monthly interest rate (r):
r = 9% / 12 = 0.09 / 12 = 0.0075

3. Total number of monthly payments (n):
n = 30 years * 12 months per year = 360 months

Now, we can substitute these values into the formula to find the monthly payment (M):

M = ($140,000 * 0.0075) / (1 - (1 + 0.0075)^(-360))

Using a calculator, we can evaluate this expression:

M ≈ $1,118.61

Therefore, the Taylors will be required to make a monthly payment of approximately $1,118.61 for their mortgage.

Answer 3

mortgage after downpayment = 140,000

i = .09/12 = .0075
n = 30(12) = 360
payment = p

p(1 - 1.0075^-360)/.0075 = 140000
p(124.2818657.) = 140000
p = $1126.47